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janhardo

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11 years, 43 days
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@salim-barzani I had created anothe...

janhardo 700
August 20 2024
0 0

@salim-barzani :  userfriendly for experimentation

A adjustable integralcurve can be set in fieldplot, with initial value point for first order ode

module_20-8-2024-Odegeneratorplots_Mprimes_A.mw

@salim-barzani  make it more richer...

janhardo 700
August 20 2024
0 0

@salim-barzani  make it more richer :-)

generatorfunctie_ode_Mprimes_postDEF_20-8-2024_var_methelp_dfieldplot_rownumber_.mw

For now the final Odegenerator procedure...

janhardo 700
August 19 2024
0 0

 @salim-barzani ,   I, made  a more userfriendly version, with help and dfieldplot ..
For now the final Odegenerator procedure for first order ode ,  with odeadvisor , DataFrame row number for the fieldplot function, adding a rownumber : A,B, and C ..is  be substituted in ODE.


generatorfunctie_ode_Mprimes_postDEF_19-8-2024_var_methelp_dfieldplot_rownumber.mw

I made a procedure out of this code ...

janhardo 700
August 18 2024
0 0

I made a procedure out of this code 
Further improvementt for a start could be a general ODE template for to generate values for the standard ODE's ( using the odeadvisor)
 

"maple.ini in users"

 (1)
> 

Odegenerator := proc(V, xi_sym, F_sym, eq_template) ## Engelse versie
    local xi, F, result, a, b, c, sol, Fsol, rows, numrows, eq, eq_check, count;

    # Initialize a list to store the rows for the DataFrame
    rows := [];

    # Counter for the number of generated printf messages
    count := 0;

    # Loop through all combinations of a, b, and c
    for a in V do
        for b in V do
            for c in V do
                # Define xi and F as the specified symbols
                xi := xi_sym;
                F := F_sym;

                # Form the differential equation by substituting the values of a, b, and c
                eq := subs({'A' = a, 'B' = b, 'C' = c}, eq_template);

                # Check the substitution
                eq_check := eval(eq);
                ### for debugging #### printf("The equation after substitution for a = %a, b = %a, c = %a is: %a\n", a, b, c, eq_check);

                # Increment the counter
                count := count + 1;

                # Solve the differential equation
                sol := dsolve(eq_check, F(xi));

                # Check if an explicit solution was found
                if type(sol, `=`) then
                    Fsol := rhs(sol);
                else
                    Fsol := "No explicit solution";
                end if;

                # Add the row to the list of rows
                rows := [op(rows), [a, b, c, Fsol]];
            end do;
        end do;
    end do;

    # Display the number of generated printf messages
    printf("Total number of printf messages generated: %d\n", count);

    # Count the number of rows (for the DataFrame)
    numrows := nops(rows);

    # Create the DataFrame with the collected rows and the correct column names
    result := DataFrame(Matrix(numrows, 4, rows), columns = ['A', 'B', 'C', F_sym(xi_sym)]);

    # Adjust the output limit to display all rows
    interface(rtablesize = numrows+10);  # Increase the limit so all rows are shown

    # Display the result
    ###printf("%A\n", result);

    return result;
end proc:

# Define the list of values for a, b, and c
V := {  0, 1/2  };  # Start with a smaller set to test

# Define the independent variable and function
xi_sym := t;
F_sym := y;

# Define the general form of the differential equation
eq_template := diff(F_sym(xi_sym), xi_sym) = 'A' + 'B'*F_sym(xi_sym) + 'C'*F_sym(xi_sym)^2;

# Call the procedure
result := Odegenerator(V, xi_sym, F_sym, eq_template);

# View the result
###result;

V := {0, 1/2}

  

xi_sym := t

  

F_sym := y

  

eq_template := diff(y(t), t) = A+B*y(t)+C*y(t)^2

  

Total number of printf messages generated: 8

  

module DataFrame () description "two-dimensional rich data container"; local columns, rows, data, binder; option object(BaseDataObject); end module

 (2)
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Download ODEgeneratorMprimesforumreactie_18-8-2024.mw


 

My procedure Fsimp uses y(t) only with p...

janhardo 700
August 13 2024
0 0

My procedure Fsimp uses y(t) only with prime notation, so maybe i can make more general later on, with a fix for de odetest
I like the most @nm 9421 , because the assumption is applied to see on g 

 

Added method:  Odesolve for finding...

janhardo 700
August 13 2024
0 0

Added method:  Odesolve for finding functions with odetest, method= laplace, series and ics 
Odesolve method will be skipped for leafcount and length calculaton ( via a list of exceptions for  skipped methods)
Using prime notation 
Added method: ODEplotseries , makes a direction field with approximation curve (series) ( polynome)
Odetest must be working 100 % ?

FSimp-integration-assuming_Mprimes_17-8-2024DEF_.mw

@MaPal93 I ask maple coding expert ...

janhardo 700
August 09 2024
0 0

@MaPal93 
I ask maple coding expert ...

@nm "Why is simplify needed to...

janhardo 700
August 07 2024
0 0

@nm 
"Why is simplify needed to evaluate limit? Is this documented somewhere?"

Because if x = 0 , b remains and a simplify command with assuming option is also possible.
It may be that the simplify algorithm first simplifies the limit question to b? 

"I do not expect that Maple covers ...

janhardo 700
July 29 2024
0 0

"I do not expect that Maple covers everything in teaching"
Well, given the effort Maplesoft is doing for education, so i thought i show my practical examples and wondering.
Jan Douma B Ed math

Maple uses the  form  [&n...

janhardo 700
July 29 2024
0 0

Maple uses the  form  [ infinity/- infinity]  for  L'Hopital to use  as derived  in another picture , but what is the educational value of this L'Hopital rule ?

Same limit , but  now form [ i...

janhardo 700
July 29 2024
0 0

Same limit , but  now form [ infinity/- infinity], and Maple goes not further to try to get the value of the limit
This is another form  [ infinity,- infinity]  for  L'Hopital to use 
  

Maple is using SimplifySteps (number 8 i...

janhardo 700
July 29 2024
0 0

Maple is using SimplifySteps (number 8 in FSimp procedure) here and shows that numerator and denominater are 0 
So, its [0/0]  
But nothing happens further and it should be interesting if L'Hopital is applied and a new limit is calculated 
Limit(-2*x^2*ln(x)^2, x = 0, right), but this is the same situation as for the startlimit 
Another trick is needed.
Perhaps with RuleSteps i get a new( but useless) limit  for the [0,0] ?
------------------------------------
Concerns me if Maple wants to be educational and show in steps of a solution , then also all the steps can be seen in a solution
--------------------------------------



In my FSimp procedure i did SimplifyStep...

janhardo 700
July 28 2024
0 0

In my FSimp procedure i did SimplifySteps on a limit and in my textbook example l'hopital
Seems to be not clear what l'hopital version is used by Maple ( there are two versions [0/0],[infinity/infinity] )


voorbeeld_Mprimesforum_limiet_lhopital.mw


 

 

@vv In the most right limit you can...

janhardo 700
July 27 2024
0 0

@vv 
Thanks, In the most right limit you can recognize some standardlimits 
But how do you know when to use l'hopital ?

With this little investigation ...
But x.ln x for x->0  gives [ 0, infinity ]  = lim x<- 0  x/ 1/ln x = [0/0] (=l'hopital)

lim x<- 0  1/ (- 1/ ln^2.x). 1/x (l'hopital applied, but it seems to go to limit x<--0  gives   x ln x^2 
Its not going better now with this limit

So we need to rewrite  x.ln x again on a second way...

Tried to add limit rules, but don't ...

janhardo 700
July 26 2024
0 0

Tried to add limit rules, but don't know how to handle the Calculus1 infolevel 1 and assigning exactly Calculus 1 package with the Uses cmmand  

FSimp-integration-assuming_Mprimes_26-7-2024.mw

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